Krishna
0

Step 1: Remember the Formula to calculate radius R of the circumscibed circle an isosceles triangle

NOTE: Radius R of the circumscibed circle an isosceles triangle of base b

and lateral side a are given by

R = \frac{a^2}{\sqrt{4a^2 - b^2}}

Step 2: Find the relationship between h, b and a (Pythagoras in triangle)

NOTE: Divide the Isosceles triangles into two right triangles.

a^2 = (\frac{b}{2})^2 + h^2

Step 3: Rewrite the relation in height

4h^2 = 4a^2 - b^2

Step 4: Replace  4 a^2 - b^2  by 4 h^2 in the

formula for R

R = \frac{a^2}{\sqrt{4 h^2}}

Step 5: Find the base of the triangle by substituting the known values in the above equation.

NOTE: R = \frac{a^2}{\sqrt{4 h^2}}

R * \sqrt{4 h^2} = a^2

Height h = 16 cm and Radius R = 9 cm

\sqrt{4 * (16)^2} * 9 = a^2

2* 16 * 9 = a^2

a = 12\sqrt{2}

Step 6: Substitute the base (a) value in the formula for the lateral side.